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General Engineering Dimensional Analysis

  1. Jan 17, 2012 #1
    The period T of a pendulum of length L, mass m in a gravitational field g ms-2 is suspected to be a function of L, m and g. If it is postulated that
    T=KLxmygz
    where K is a dimensionless constant, use dimensional analysis to obtain the constants x, y and z.

    There's only one pi group I came up with and that was g/(T2L)

    other than that, I can't figure out how to begin this problem in a way that will give me an opportunity to solve for the three exponents.
     
  2. jcsd
  3. Jan 17, 2012 #2
    Start by writing out the dimensions (mass, length, time) of each of the physical quantities involved.
     
  4. Jan 17, 2012 #3
    Ok so perhaps my attempt wasn't completely written above. I wrote down all the units, namely meters, m/s^2 for gravity and kg for mass. That's the only pi group I can think of but then I can't figure out the steps to solve for 3 individual exponents.
     
  5. Jan 17, 2012 #4
    how about for T?
     
  6. Jan 17, 2012 #5
    Well T=1/s which is included in my original Pi group of g/(T^2*L). But once I have one pi group, which is all I can have because I have 4 variables and only 3 basic dimensions, how do I go about relating that to solving for the variables?

    Correct me if I'm wrong, but mass should not play a factor in pendulum swings. And should I use the pendulum period equation from basic physics, neglecting drag etc.?
     
  7. Jan 17, 2012 #6
    Ok, first of all, what is a "Pi group"?

    Second, your dimension (unit) for the PERIOD T is incorrect?
     
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